Question 1113287
f = p * (1 + r) ^ n


f is the future value
p is the present value
r is the interest rate per time period.
n is the number of time periods.


to find the interest earned, you would then subtract the present value from the future value.


the formula for that would be:


i = f - p


solve this equation for f to get:


f = p + i


in your problem:


p = 2900
f = p + i = 2900 + 500 = 3400
i = .08 / 12 per month.
n = number of months.


your equation becomes:


3400 = 2900 * (1 + .08/12) ^ n


divide both sides of this equation by 2900 to get:


3400 / 2900 = (1 + .08/12) ^ n


take the log of both sides of this eqution to get:


log(3400 / 2900) = log((1 +.08/12) ^ n)


since log (b^x) = x * log(b), this equation becomes:


log(3400 / 2900) = n * log(1 + .08/12)


solve for n to get:


n = log(3400 / 2900) / log(1 + .08/12) = 23.93914847 months.


replace n in the original equation with that to confirm the solution is correct.


original equation becomes 3400 = 2900 * (1 + .08/12) ^ 23.93914847.


this results in 3400 = 3400, confirming the solution is correct.


23.93914847 months / 12 = 1.994929039 years.


round this to the nearest tenth of a year to get 2 years.